RELATIVE DEFORMATION THEORY, RELATIVE SELMER GROUPS, AND LIFTING IRREDUCIBLE GALOIS REPRESENTATIONS

We study irreducible odd mod p Galois representations (rho) over bar: Gal((F) over bar /F)-> G((F) over bar (p)), for F a totally real number field and G a general reductive group. For p >>(G,F) 0, we show that any (rho) over bar that lifts locally, and at places above p to de Rham and Hodge-Tate regular representations, has a geometric p-adic lift. We also prove non-geometric lifting results without any oddness assumption.

Automated summary

The study focuses on irreducible odd mod p Galois representations, investigating the properties of representations locally and at places above p, and proving related conclusions.